Chapter 12, Problem 20CR

To determine

To calculate: The value of x in parallelogram ABCD .

Answer to Problem 20CR

The value x is ${65}^{\circ }$ .

Explanation of Solution

Given information:

  $\angle D={40}^{\circ }.$

Angles ${150}^{\circ }$ and ${35}^{\circ }$ are also given.

Calculation:

  

∠1 is supplementary to ${150}^{\circ }$ ,

  $\angle 1={30}^{\circ }$

By property of alternate interior angles,

  $\angle 2={30}^{\circ }$

Angles 2, 3 and ${35}^{\circ }$ form a triangle.

  $\angle 3=180^o-35^o-30^o$

∠x is supplementary to ${115}^{\circ }$ ,

So $\angle x={65}^{\circ }$